TSTP Solution File: NUM750^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM750^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 13:56:04 EDT 2022
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_frac,type,
frac: $tType ).
thf(ty_pf,type,
pf: frac > frac > frac ).
thf(ty_z,type,
z: frac ).
thf(ty_y,type,
y: frac ).
thf(ty_eq,type,
eq: frac > frac > $o ).
thf(ty_x,type,
x: frac ).
thf(sP1,plain,
( sP1
<=> ! [X1: frac] : ( eq @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eq @ x @ y )
=> ( ( eq @ z @ z )
=> ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: frac,X2: frac,X3: frac] :
( ( eq @ x @ X1 )
=> ( ( eq @ X2 @ X3 )
=> ( eq @ ( pf @ x @ X2 ) @ ( pf @ X1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eq @ z @ z ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP4
=> ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: frac,X2: frac] :
( ( eq @ x @ y )
=> ( ( eq @ X1 @ X2 )
=> ( eq @ ( pf @ x @ X1 ) @ ( pf @ y @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: frac,X2: frac,X3: frac,X4: frac] :
( ( eq @ X1 @ X2 )
=> ( ( eq @ X3 @ X4 )
=> ( eq @ ( pf @ X1 @ X3 ) @ ( pf @ X2 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: frac] :
( ( eq @ x @ y )
=> ( ( eq @ z @ X1 )
=> ( eq @ ( pf @ x @ z ) @ ( pf @ y @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eq @ x @ y ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(satz62b,conjecture,
sP8 ).
thf(h0,negated_conjecture,
~ sP8,
inference(assume_negation,[status(cth)],[satz62b]) ).
thf(1,plain,
( ~ sP1
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP7
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP3
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP6
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP9
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP2
| ~ sP10
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP5
| ~ sP4
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(e,axiom,
sP10 ).
thf(satz56,axiom,
sP7 ).
thf(satz37,axiom,
sP1 ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,e,satz56,satz37,h0]) ).
thf(0,theorem,
sP8,
inference(contra,[status(thm),contra(discharge,[h0])],[8,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM750^1 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jul 6 11:50:21 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % Mode: mode213
% 0.12/0.36 % Inferences: 6
% 0.12/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------